It seems reasonable that instructors should be able to access an "archive" or something similar to review graded assignments. This is true but it is not as easy to find as you might think it should be.
STEP 1: Log into your Blackboard course and from the Control Panel (lower left of your screen) open up Grade Center and can select the downward facing arrows in the column for the assignment and that lines up with the students name (like the image below).
STEP 2: Then select view attempt (or view details and view the attempt you wish to see).
STEP 3: After clicking on the attempt (view image above), the next page you see will have a link to the students submitted work or document.